Assume that $X=X_1 + X_2 +...+X_n$, where $X_i \sim CN(0,\sigma^2)$ and independent. Here $CN$ means circular complex Gaussian.

The question is, what is the distribution for

$Z = \frac{\left|X\right|^2}{\left|X_1\right|^2 + \left|X_2\right|^2+...+\left|X_n\right|^2}$

How can we benefit from the results obtained here: Distribution of the ratio of dependent chi-square random variables

  • $\begingroup$ Is this question from a course or a textbook? If so, please add the [self-study] tag & read its wiki. $\endgroup$ – gung - Reinstate Monica Feb 11 '15 at 6:43
  • $\begingroup$ @gung. No, this question is not from any class. $\endgroup$ – mustafa Feb 11 '15 at 18:45

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